Inside Da' Barber Shop on Detroit's east side, the city's financial troubles are topic No. 1. But the possibility that the predominantly African-American city could elect its first white mayor in 40 years isn't far behind.

"White people gave Obama a chance. Maybe it's time for a change for us, too," said owner Will Kinney, a 45-year-old lifelong Detroiter who said he worries about the city's violent crime and rampant...